Between the two the highlighted spec is the better choice for one simple reason the GPU..you will mostly likely play not only sto but other games and having a higher spec GPU will give you that room to play them. the third gen intel chips are more for work stations rathern than gaming machines you want the sandy bridge-E series of i5's and i7's.
I would most likely build your own if you want a good gaming computer.I would not bye any store bought ones as they are loading tons of junk on them.With your own build you can pick witch parts you want and probably save a little money on it rather spend a good 1,000 on a store bought one.I built mine for under a 1,000.Video card was the most costly part.
Everyone is giving good advise. Whatever you do go with, at least use NVidia GTX560i or better, Dual-Core i3 or better, the rest does not matter.
I don't have time to play any other game so I specifically built my system with a mid-line motherboard (meaning not the "best of the best") of a good name and could take 3rd Gen Intel CPUs. 8GB RAM, GTX560i, Intel i3 2nd Gen CPU (cheapest I could get), an 80 GB hard drive I already had. Windows 7 64-bit Home Ed. It runs GREAT at FULL Quality!
If you plan to play other games, then you want to match the systems specs with those games. STO is not hardware intensive besides the GPU/video card.
Intels are good, but usually overpriced. If you get the AMD equivalent you will save some money and be just as happy.
The 2nd option is better mainly because of the video card. the first one had a 620 which isn't high end at all. If you go with an Nvidia card, I would not recommend going with anything less than an X40 (440, 540, 640, etc) as you won't be happy with anything less. If money is not a problem, go with option 2 as that card will handle the game on ultra settings without issue. In fact, that card may be a little overkill.
I run a GTX 560 on max settings and it performs wonderfully.